429.75=t^2+50t

Solution for 429.75=t^2+50t equation:

429.75=t^2+50t

We move all terms to the left:

429.75-(t^2+50t)=0

We get rid of parentheses

-t^2-50t+429.75=0

We add all the numbers together, and all the variables

-1t^2-50t+429.75=0

a = -1; b = -50; c = +429.75;
Δ = b2-4ac
Δ = -502-4·(-1)·429.75
Δ = 4219
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-\sqrt{4219}}{2*-1}=\frac{50-\sqrt{4219}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+\sqrt{4219}}{2*-1}=\frac{50+\sqrt{4219}}{-2}
$